Stabilizer Rényi Entropy Without a Phase Reference
Abstract
Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for n channels is ln[n3/(6n−5)] for n≥3 and ln7/5 for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: ln7/5 at four points and ln27/13 in 3→2 scattering. In same-helicity 2→3 scattering, it lies between a floor of ln8/7 and a ceiling of ln184/125, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.
Related
- Rényi Multi-entropy for Stabilizer States: A Finite Field Gauss Sum Problem
- Fast and exact approach for stabilizer Rényi entropy via the XOR-FWHT algorithm
- Efficient Pauli Truncation from Operator Stabilizer Rényi Entropy
- Classical Root Systems Reveal Defect-Junction Data in Stabilizer Rényi Entropy
- Finite-size scaling theory of Rényi thermal entropy for second-order, first-order, and weakly first-order quantum phase transitions
BibTeX
@misc{chu2026stabilizer,
title = {{Stabilizer Rényi Entropy Without a Phase Reference}},
author = {Jinwei Chu and Savan Kharel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18955},
eprint = {2610.18955},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18955},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stabilizer Rényi Entropy Without a Phase Reference
AU - Jinwei Chu
AU - Savan Kharel
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18955
UR - https://arxiv.org/abs/2610.18955
AB - Stabilizer Rényi entropy quantifies magic relative to a complete Pauli frame. In settings such as helicity states of massless particles, unsynchronized qubit registers, energy eigenbases, and systems under superselection rules, the computational basis may be fixed while the transverse Pauli axes remain unspecified. The stabilizer Rényi entropy then depends on the choice of those axes. We define a phase-averaged stabilizer Rényi entropy by averaging the Pauli moments before taking the logarithm. It is exactly invariant under independent local rephasings. For pure states, it vanishes precisely when the state is a stabilizer state in every phase convention. For a broad class of sparse supports, it reduces to a closed-form function of the basis-state probabilities alone. Within this class, the ceiling for n channels is ln[n^3/(6n−5)] for n≥3 and ln7/5 for two channels. We apply the invariant to tree-level gluon scattering at four and five points, where the helicity-basis phases are unspecified. It saturates the two- and three-channel ceilings: ln7/5 at four points and ln27/13 in 3→2 scattering. In same-helicity 2→3 scattering, it lies between a floor of ln8/7 and a ceiling of ln184/125, reached in the resolved soft limit and particular collinear limits, respectively. In every configuration studied, the invariant is independent of the fixed external colors.
ER -